Family
One of the major themes in the film is family. Throughout the film we see Billy and his family members having trouble connecting to one another, and having to find allegiance to one another in spite of their huge differences. After the loss of his wife, Jackie is determined to keep his family together, but he often has trouble understanding and accepting his sons, providing the nurturance that their mother did. Throughout much of the film, he hates the idea of Billy becoming a dancer and actively tries to thwart Billy's dream, but he ultimately realizes that his son has an amazing talent and eventually works hard to give him the opportunity to go to ballet school. Tony, too, becomes supportive of Billy's passion, and they work hard to help give Billy the opportunity to escape their small town. While the beginning of the film paints a portrait of a fragmented family, one whose members do not support or understand one another, eventually it becomes a film about the power of love in a family, and how even in turmoil, family can come together.
Passion
Throughout the film, we see Billy dancing almost in spite of himself, and at times, he cannot help but kick his feet in the air and do a dance. All of these instances demonstrate his passion for dancing, the fact that it is an insistent urge throughout his life. In moments when life seems hard to bear, Billy turns to dance, and movement bubbles up in his body at key moments in his life.
Later in the film, when it seems that he has almost ruined his chances of going to ballet school, he answers a question posed by the judges by saying that dancing is a sensation of having electricity running through his body. His description, so visceral and passionate, catches the attention of the judges. While he is not the typically polished or posh student of the ballet school, he demonstrates a passion that is unique and special.
Class
Ballet dancers don't typically come from little mining villages in the north of England. Class is a major theme of Billy Elliot, as part of what makes Billy's interest in ballet so disruptive to his family and his community is not only that he is a boy in a girl's discipline, but that he is a poor boy in a rich boy's discipline. His father is a simple miner, fighting for the rights of the worker, but Billy just wants to dance, a pastime that is perceived as frivolous. Billy's mismatch with ballet is put into contrast when he goes to audition for ballet school and finds himself surrounded by much wealthier applicants, even punching one of them that is too friendly to him. The theme of class is not directly addressed, but it informs Billy's narrative in the film.
Politics
The film is set against the backdrop of the miners' strike in Northern England that occurred in the 1980s, a battle between the unions and the government under Margaret Thatcher. Jackie and Tony are both miners who are on strike for their beliefs. While they share many of the same beliefs, we see them come into conflict about certain details of the movement. Jackie doesn't like how violent and radical Tony has become, while Tony sees his father as passive and not fighting hard enough. On the occasion of Billy's first audition for ballet school, Tony gets arrested and Billy has to miss his audition. Thus political conflict is a major theme in the film, as we see that Billy's interest in ballet is set in stark contrast to the heated political issues of the times.
Gender
Gender is at the center of Billy's problems, even though he sees no issue with his interest in ballet. In the town where he is from, boxing is for boys and ballet for girls, yet Billy's deep love for dance draws him towards ballet nonetheless. At first, he himself is confused about whether his interest in ballet belies some kind of effeminacy, but soon learns that male ballet dancers are some of the most athletic men in the world, which reassures him.
Even though it doesn't take Billy long to learn that ballet doesn't make him less of a man, it takes his brother and father awhile longer to catch up to him. They are convinced that ballet is for women and gay men, and their bigoted attitudes prevent them from seeing Billy's immense talent. Their perceptions of gender prevent them from accepting what is right before their eyes.
Additionally, Billy's best friend Michael is coming to terms with being gay, experimenting with cross-dressing and his own effeminacy. While Billy's discipline of choice, ballet, marks him as subverting gender expectations, Michael grapples with the fact that he isn't like other boys in key ways. Billy, an ever-sympathetic protagonist, accepts Michael and encourages his friend's effeminacy, bringing him up to the gymnasium after hours and putting him in a tutu.
Loss
A shadow hanging over Billy's life from the start of the film is the loss of his mother. After his mother died, he has been left in the charge of his confused and overwhelmed father, who struggles to provide the nurturance that Billy's mother no longer can. As we also discover early on, Billy was encouraged by his mother to pursue his artistic interests, but Jackie does not approve of Billy's dreamier sensibilities. Thus, Billy's pursuit of ballet becomes a way for him to keep his mother's memory alive. The film includes a few references to loss. In one scene, Billy goes into the fridge at night and meets a vision of his mother, a memory of how she would have gently reminded him to clean up after himself. He wishfully imagines that his mother is still there, telling him what to do.
Acceptance
The point on which the narrative turns is Jackie (and the mining community at large) coming to accept Billy's unique interest in dance. While Jackie had previously railed against Billy's predisposition and blatantly forbidden him from pursuing dance, he changes his tune after he sees Billy dance defiantly in the gymnasium one night. All it takes is a moment seeing how talented and passionate his son is, and Jackie has a completely different feeling about Billy's interest, going immediately to Sandra's house to ask about their options. The moment is somewhat unbelievable in its abruptness—the stuff of movies—but it marks a seismic shift in the course of Billy's life. With the acceptance of his father and brother—his greatest barriers to pursuing ballet—Billy is closer not only to realizing his own potential, but to connecting with his family.